(6 points for the correct answer; 2 bonus point if you have…
(6 points for the correct answer; 2 bonus point if you have correctly answered a total of 9 questions among questions 1 through 11.) Consider the following proof of the fact that the sum of any two even integers is even: Suppose and are any even integers. By definition of even, and for some integers and . Then . Note that is an integer because the sum of two integers is an integer. Hence is an even integer by definition of even. Is the proof valid?
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(6 points for the correct answer; 2 bonus point if you have correctly answered a total of 9 questions among questions 1 through 11.) Consider the following proof of the fact that the product of any two odd integers is odd: Suppose and are any odd integers. By definition of odd, and for some integers and . Then . Note that is an integer because the sums and products of integers are integers. Hence is an odd integer by definition of odd. Is the proof valid?
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